oppurtunity to earn ten pts.?

Question

1).u can write a^(n)-b^(n)=c^(2)-d^(2)
here a,b,c&d are natural & real numbers.n is a natural number.
like 7^(3)-4^(3)=48^(2)-45^(2)
2).u can also write for any number say x having any power say
n can also be written as
x^(n)=y^(2)-z^(2)
here x ,y & z are natural & real numbers
like 3^(3)=14^(2)-13^(2)
from this show that it is impossible to write
a^(n)-b^(n)=x^(n) for n>=2.

Answer 1

The problem you are asking is generalized Pythagoras theorem or (more commonly known amidst mathematicians as) Fermat's last theorem. The theorem was, at last, proved by Andrew Wiles. The problem has only one (trivial) solution viz x=0,a=0,b=0.

Answer 2

From your question N can equal 2

(n>=2)

5^2-4^2=3^2
13^2-12^2=5^2

There are an infinity of solutions - I think you better
restate your problem.

Answer 3

the proof that u asked is the proof for fermats last theorem(or lost theorem as the proof for it written by fermat was never found).it states that a^n+b^n=c^n doesnt exist for n>2.
the proof for this theorem however cannot fit this page(though there are doubts today that fermat even had a proof for this theorem).the proof was however formulated by two others namely Andrew Wiles and Richard Taylor in October 1994
the following site should help u
http://en.wikipedia.org/wiki/fermats_last_theorem

Answer 4

a^2 - b^2 = (a+b)(a-b)
set b = a then
a(a-a) = (a+a)(a-a)
now cancel common term on both sides
a = a+a
a = 2a
1 =2 Voila

Answer 5

hi...rajesh...
wat r u askin man...??? dis ques bounced on my head... Plz ask some easy ques....

Answer 6

see : http://answers.yahoo.com/question/index;_ylt=AjrpBOa_rpnanPOL7fpq1q7sy6IX?qid=20060725055335AAsawz3

btw it is n > 2

Answer 7

MAD CAP